Classical theory of collective motion in the large amplitude, small velocity regime

A classical theory of collective motion is developed for the large amplitude, small velocity limit, i.e., for a hamiltonian that is at most quadratic in the momenta, allowance being made for a mass tensor that is a general function of the coordinates. It is based on the identification of decoupled motions that are confined to submanifolds of the full configuration space. Conditions for decoupling are derived and then transformed into several different sets of equivalent conditions, more useful for practical applications. Algorithms are given for constructing manifolds that are exactly decoupled if a given dynamical system admits such motions and that can be utilized as well when there is approximate decoupling, as evidenced by criteria that are established. Some examples are worked out. The connection to previous research on this problem is described.